Vladimir Kanovei

Q: What Schools Are Affiliated With Vladimir Kanovei

Vladimir Kanovei is affiliated with the following schools: Moscow State University, Russian University of Transport

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Vladimir Kanovei

Mathematics

#3017

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#4539

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Real Analysis

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#17

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Measure Theory

#2942

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#3495

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Mathematics

Vladimir Kanovei's Degrees

PhD Mathematics Moscow State University

Why Is Vladimir Kanovei Influential?

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According to Wikipedia, Vladimir G. Kanovei is a Russian mathematician working at the Institute for Information Transmission Problems in Moscow, Russia. His interests include mathematical logic and foundations, as well as mathematical history.

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Vladimir Kanovei's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Undecidable hypotheses in Edward Nelson's internal set theory (1991) (114)
Borel equivalence relations : structure and classification (2008) (97)
Nonstandard Analysis, Axiomatically (2004) (93)
A definable nonstandard model of the reals (2003) (59)
Canonical Ramsey Theory on Polish Spaces (2013) (55)
Is mathematical history written by the victors (2013) (45)
Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow (2014) (41)
Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics (2012) (40)
Interpreting the Infinitesimal Mathematics of Leibniz and Euler (2016) (37)
Approaches to analysis with infinitesimals following Robinson, Nelson, and others (2017) (35)
On non-wellfounded iterations of the perfect set forcing (1999) (29)
On some classical problems of descriptive set theory (2003) (28)
Internal approach to external sets and universes (1995) (26)
Internal approach to external sets and universes (1996) (25)
A definable E0 class containing no definable elements (2014) (25)
An Ulm-type classification theorem for equivalence relations in Solovay model (1997) (25)
The correctness of Euler's method for the factorization of the sine function into an infinite product (1988) (24)
Leibniz versus Ishiguro: Closing a Quarter Century of Syncategoremania (2016) (24)
A model of second-order arithmetic satisfying AC but not DC (2018) (23)
Toward a History of Mathematics Focused on Procedures (2016) (23)
MATHEMATICS IN A NONSTANDARD WORLD I (1997) (21)
Proofs and Retributions, Or: Why Sarah Can’t Take Limits (2015) (20)
A Groszek‐Laver pair of undistinguishable E0 ‐classes (2016) (19)
Internal approach to external sets and universes (1995) (18)
When a partial Borel order is linearizable (1997) (18)
Counterexamples to countable-section Π12 uniformization and Π13 separation (2015) (18)
Definable E0 classes at arbitrary projective levels (2017) (17)
New Radon-Nikodym ideals (2000) (16)
Euler’s Lute and Edwards’s Oud (2015) (16)
Gregory’s Sixth Operation (2016) (14)
Kolmogorov's ideas in the theory of operations on sets (1988) (14)
Non-uniformizable sets of second projective level with countable cross-sections in the form of Vitali classes (2018) (13)
Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy (2017) (13)
Controversies in the Foundations of Analysis: Comments on Schubring’s Conflicts (2016) (13)
Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms (2017) (13)
L O ] 1 8 A ug 2 01 4 A countable definable set of reals containing no definable elements (2014) (13)
DEFINABLE MINIMAL COLLAPSE FUNCTIONS AT ARBITRARY PROJECTIVE LEVELS (2017) (12)
A countable definable set containing no definable elements (2014) (12)
Intermediate models of Prikry generic extensions (2010) (12)
A Non-Standard Analysis of a Cultural Icon: The Case of Paul Halmos (2016) (11)
Uniqueness, collection, and external collapse of cardinals in IST and models of Peano arithmetic (1995) (11)
Non-Glimm–Effros equivalence relations at second projective level (1997) (11)
On Baire Measurable Homomorphisms of Quotients of the Additive Group of the Reals (2000) (11)
NIKOLAI NIKOLAEVICH LUZIN: The development of the descriptive theory of sets under the influence of the work of Luzin (1985) (11)
On the Nonemptiness of Classes in Axiomatic Set Theory (1978) (11)
Continuity between Cauchy and Bolzano: issues of antecedents and priority (2020) (10)
Models of set theory in which the separation theorem fails (2019) (10)
Cauchy, infinitesimals and ghosts of departed quantifiers (2017) (10)
Some new results on Borel irreducibility of equivalence relations (2002) (10)
Ulm Classification of Analytic Equivalence Relations in Generic Universes (1998) (10)
UNDECIDABLE AND DECIDABLE PROPERTIES OF CONSTITUENTS (1985) (9)
Problems of set-theoretic non-standard analysis (2007) (9)
What Makes a Theory of Infinitesimals Useful? A View by Klein and Fraenkel (2018) (9)
An unpublished theorem of Solovay on OD partitions of reals into two non-OD parts, revisited (2020) (9)
A Nonstandard Proof of the Jordan Curve Theorem (1996) (9)
Isomorphism Property in Nonstandard Extensions of the ZFC Universe (1996) (9)
Generalization of one construction by Solovay (2015) (9)
On a Glimm -- Effros dichotomy and an Ulm--type classification in Solovay model (1995) (8)
On mathematical realism and applicability of hyperreals (2019) (8)
Small oscillations of the pendulum, Euler’s method, and adequality (2016) (8)
MINIMAL AXIOMATIC FRAMEWORKS FOR DEFINABLE HYPERREALS WITH TRANSFER (2017) (8)
Two dichotomy theorems on colourability of non-analytic graphs (1997) (8)
Borel and Countably Determined Reducibility in Nonstandard Domain (2002) (8)
On coding uncountable sets by reals (2010) (7)
Linearization of Definable Order Relations (1997) (7)
Cauchy's Work on Integral Geometry, Centers of Curvature, and Other Applications of Infinitesimals (2020) (7)
Topologies generated by effectively Suslin sets, and their applications in descriptive set theory (1996) (7)
Countable OD sets of reals belong to the ground model (2016) (7)
19th-century real analysis, forward and backward (2019) (7)
Cardinality of the set of Vitali equivalence classes (1991) (7)
Models of Set Theory in which Nonconstructible Reals First Appear at a Given Projective Level (2020) (6)
An infinity which depends on the axiom of choice (2012) (6)
A Generic Property of the Solovay Set Σ (2016) (6)
Counterexamples to countable-section uniformization and separation (2014) (6)
An effective minimal encoding of uncountable sets (2011) (6)
On Harrington's model in which Separation holds but Reduction fails at the 3rd projective level, and on some related models of Sami (2018) (6)
Grossone approach to Hutton and Euler transforms (2015) (6)
The axiom of determinacy and the modern development of descriptive set theory (1988) (5)
Effective compactness and sigma-compactness (2011) (5)
On external Scott algebras in nonstandard models of Peano arithmetic (1996) (5)
Borel OD sets of reals are OD-Borel in some simple models (2018) (5)
THE SET OF ALL ANALYTICALLY DEFINABLE SETS OF NATURAL NUMBERS CAN BE DEFINED ANALYTICALLY (1980) (5)
Do stronger definitions of randomness exist? (2003) (5)
On effective σ‐boundedness and σ‐compactness (2011) (5)
Is Leibnizian Calculus Embeddable in First Order Logic? (2016) (5)
A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory (2017) (4)
The full basis theorem does not imply analytic wellordering (2017) (4)
On Borel orderable groups (2001) (4)
On the ‘Definability of Definable’ Problem of Alfred Tarski (2020) (3)
On a Glimm -- Effros dichotomy theorem for Souslin relations in generic universes (1995) (3)
Extending Standard Models of ZFC to Models of Nonstandard Set Theories (2000) (3)
Some natural equivalence relations in the Solovay model (2008) (3)
A theorem on ROD‐hypersmooth equivalence relations in the Solovay model (2003) (3)
Definable Elements of Definable Borel Sets (2019) (3)
A generalization of Solovay's $\Sigma$-construction (2014) (3)
On the Δ n 1 Problem of Harvey Friedman (2020) (3)
Theory of zermelo without power set axiom and the theory of Zermelo-Frenkel without power set axiom are relatively consistent (1981) (3)
Definable Hamel bases and AC ω ( R ) (2019) (3)
Loeb Measure from the Point of View of a Coin Flipping Game (1996) (3)
On the Set of Constructible Reals (2004) (2)
On effective σ-boundedness and σ-compactness in Solovay’s model (2015) (2)
On the Equality Relation Modulo a Countable Set (2020) (2)
On Hausdorff ordered structures (2009) (2)
A version of the Jensen–Johnsbråten coding at arbitrary level n≥ 3 (1997) (2)
A countable definable set containing no definable elements (2017) (2)
On "star" schemata of Kossak and Paris (1998) (2)
Borel reducibility of equivalence relations (2008) (2)
In Cohen generic extension, every countable OD set of reals belongs to the ground model (2016) (2)
OD elements of countable OD sets in the Solovay model (2016) (2)
On intermediate extensions of generic extensions by a random real (2018) (2)
A confinal family of equivalence relations and Borel ideals generating them (2006) (2)
On the 1n Problem of Harvey Friedman (2020) (2)
A nonstandard set theory in the $\displaystyle\in$-language (2000) (2)
On Effectively Indiscernible Projective Sets and the Leibniz-Mycielski Axiom (2021) (2)
Nonstandard Set Theory in ∈-Language (2001) (2)
A Model in Which the Separation Principle Holds for a Given Effective Projective Sigma-Class (2022) (2)
Bounding and decomposing thin analytic partial orderings (2014) (2)
Lebesgue measure and gambling (2008) (1)
On a Spector Ultrapower for the Solovay Model (1995) (1)
Proof of a theorem of Lusin (1978) (1)
Linear ROD subsets of Borel partial orders are countably cofinal in Solovay's model (2010) (1)
A weak dichotomy below E1×E3 (2007) (1)
Hyperfinite equivalence relations (2008) (1)
Summation of divergent series from the nonstandard piont of view (1995) (1)
L O ] 3 S ep 2 01 8 A countable definable set of reals containing no definable elements ∗ (2018) (1)
Varia. Ideals and Equivalence Relations (2006) (1)
On countable cofinality of definable chains in Borel partial orders (2013) (1)
Part 2 External universes over the universe of bounded set theory (1995) (1)
Is Pluralism in the History of Mathematics Possible? (2022) (1)
A Generic Model in Which the Russell-Nontypical Sets Satisfy ZFC Strictly between HOD and the Universe (2022) (1)
Structure of constituents of Π11-sets (1983) (1)
Other nonstandard theories (2004) (1)
On the ‘Deﬁnability of Deﬁnable’ Problem of Alfred Tarski (2020) (1)
Elementary Extensions of External Classes in a Nonstandard Universe (1998) (1)
N. N. Luzin's problems on imbeddability and decomposability of projective sets (1982) (1)
Historical Infinitesimalists and modern historiography of infinitesimals (2022) (1)
to External Sets and Universes Part 3 Partially saturated universes (1996) (1)
Problem of the existence of nonBorel AF∥-sets (1985) (1)
Is Leibnizian Calculus Embeddable in First Order Logic? (2016) (1)
On a dichotomy related to colourings of definable graphs in generic models (1996) (1)
N. N. Luzin's problems on the existence of CA-sets without perfect subsets (1987) (1)
Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms (2017) (1)
On countable cofinality and decomposition of definable thin orderings (2014) (1)
IST is more than an algorithm to prove ZFC theorems (1993) (1)
On the extension principle in internal set theory (1992) (0)
F eb 2 01 9 Definable Hamel bases and AC ω ( R ) (2019) (0)
Borel irreducibility between two large families of Borel equivalence relations (2016) (0)
The parameterfree Comprehension does not imply the full Comprehension in the 2nd order Peano arithmetic (2022) (0)
Namur Is mathematical history written by the victors ? (0)
J ul 2 01 4 Bounding and decomposing thin analytic partial orderings ∗ (2014) (0)
Descriptive set theoretic background (2008) (0)
Gregory’s Sixth Operation (2016) (0)
On the Equality Relation Modulo a Countable Set (2020) (0)
Canonization of Smooth Equivalence Relations on Infinite-Dimensional E0-Large Products (2018) (0)
Factoring Solovay-random extensions, with application to the reduction property (2020) (0)
A definable E0 class containing no definable elements (2015) (0)
Monotone subsequence via ultrapower (2018) (0)
More on countable equivalence relations (2008) (0)
Product-type ideals (2013) (0)
A weak dichotomy below E 1 × E 3 (2010) (0)
A generalization of Solovay's -construction with application to intermediate models ∗ (2014) (0)
Turbulent group actions (2008) (0)
Forcing extensions of the nonstandard universe (2004) (0)
Perfect subsets of invariant CA-sets (2005) (0)
On initial segments of degrees of constructibility (1975) (0)
A generalization of Solovay's -construction ∗ (2015) (0)
A consequence of the Martin axiom (1979) (0)
Definable selector for $\bf\Delta^0_2$ sets modulo countable. (2019) (0)
Definable Hamel bases and ${\sf AC}_\omega ({\mathbb R})$ (2021) (0)
An answer to Luzin's question about the separability of Ca-curves (1983) (0)
A ug 2 01 4 A definable E 0 class containing no definable elements (2014) (0)
On Cohen and Gandy–Harrington forcing over countable models (2008) (0)
Borel reducibility as an additive property of domains (2009) (0)
On nonwellfounded iterated Sacks extensions, with application to the Glimm -- Effros property (1995) (0)
Benchmark equivalence relations (2013) (0)
Classes of equivalence relations (2013) (0)
Effective cardinals in the nonstandard universe (2005) (0)
A Non-Standard Analysis of a Cultural Icon: The Case of Paul Halmos (2016) (0)
On automorphisms behind the Gitik -- Koepke model for violation of the Singular Cardinals Hypothesis w/o large cardinals (2010) (0)
Actions of the infinite symmetric group (2008) (0)
Pyramidal structure of constructibility degrees (1998) (0)
Do most strong de nitions of randomness exist ? (1998) (0)
Generalization of P.S. Novikov's theorem on cross sections of Borel sets (1983) (0)
Linearization of de nable order relations( (1999) (0)
An unpublished theorem of Solovay, revisited (2020) (0)
DEVELOPMENT IN NONSTANDARD SET THEORETIC ANALYSIS (2008) (0)
A Model in Which Well-Orderings of the Reals Appear at a Given Projective Level (2022) (0)
The game ideals (2013) (0)
Factoring Solovay-random extensions, with application to the reduction property (2020) (0)
Generalization of one construction by Solovay (2015) (0)
Small oscillations of the pendulum, Euler’s method, and adequality (2016) (0)
Reasonable non–Radon–Nikodym idealss (2018) (0)
What internal set theory knows about standard sets (1997) (0)
A version of the Jensen-Johnsbr{\aa}ten coding at arbitrary level $n\geq 3$ (1997) (0)
Proofs and Retributions, Or: Why Sarah Can’t Take Limits (2014) (0)
Absoluteness of the Solovay Set Σ (2019) (0)
A nonstandard set theory in the epsilon-language (2000) (0)
Summable equivalence relations (2008) (0)
A product forcing model in which the Russell-nontypical sets satisfy ZFC strictly between HOD and the universe (2021) (0)
Elementary real analysis in the nonstandard universe (2004) (0)
Pinned equivalence relations (2008) (0)
Controversies in the Foundations of Analysis: Comments on Schubring’s Conflicts (2015) (0)
Partially saturated universes and the Power Set problem (2004) (0)
Metric completions, the Heine-Borel property, and approachability (2020) (0)
ON INITIAL SEGME'NTS OF DEGREES OF CONSTRUCTIBILITY (2004) (0)
On the complexity of finitely additive measures (1996) (0)
Foundations of infinitesimal calculus: surreal numbers and nonstandard analysis (2013) (0)
Countable OD sets of reals belong to the ground model (2017) (0)
Reduction of Borel equivalence relations to Borel ideals (2008) (0)
Ju l 2 01 9 19 TH CENTURY REAL ANALYSIS , FORWARD AND BACKWARD (0)
Definable external sets and metamathematics of HST (2004) (0)
L O ] 1 N ov 2 01 6 A generic property of Solovay ’ s set Σ (2016) (0)
Canonization of smooth equivalence relations on infinite-dimensional perfect cubes (2018) (0)
On the Significance of Parameters in the Choice and Collection Schemata in the 2nd Order Peano Arithmetic (2023) (0)
A Generic Property of the Solovay Set Σ (2017) (0)
Extension of standard models of ZFC to models of Nelson’s nonstandard set theory IST (1999) (0)
Indiscernible pairs of countable sets of reals at a given projective level. (2019) (0)
On the infinitary pantachie of Du Bois Reymond ∗ (2011) (0)
Special Model Axiom in Nonstandard Set Theory (1999) (0)
On Russell typicality in Set Theory (2021) (0)
On a dichotomy related to colourings of de nablegraphs in generic modelsVladimir (1996) (0)
Metamathematics of internal theories (2004) (0)
THE IDEAS OF N. N. LUZIN IN DESCRIPTIVE SET THEORY (2016) (0)
Ramsey-type ideals (2013) (0)
Introduction to equivalence relations (2008) (0)
The countable support iteration ideals (2013) (0)
Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics (2012) (0)
Singular cardinals (1973) (0)
Interpreting the Infinitesimal Mathematics of Leibniz and Euler (2016) (0)
Linearization of partial quasi-orderings in the Solovay model revisited. ∗ (2014) (0)
Toward a History of Mathematics Focused on Procedures (2016) (0)
The 1st and 2nd dichotomy theorems (2008) (0)
Euler’s Lute and Edwards’s Oud (2015) (0)
L O ] 1 6 O ct 2 01 4 Counterexamples to countable-section Π 1 2 uniformization and Π 13 separation (2014) (0)
Some theorems of descriptive set theory (2008) (0)
“Hyperfinite” descriptive set theory (2004) (0)
Reducibility of monadic equivalence relations (2007) (0)
A nonstandard set theory in the [mathematical formula]-language (2000) (0)
Gaps in partially ordered sets and related problems Commentary to [H 1909a] and [H 1936b] (2011) (0)
Games and the Silver property (2013) (0)
Effective compactness and sigma-compactness (2012) (0)
Ju n 20 13 IS MATHEMATICAL HISTORY WRITTEN BY THE VICTORS ? (2013) (0)
Counterexamples to countable-section Π 2 1 uniformization and Π 3 1 separation (2016) (0)
Analytic equivalence relations and models of set theory (2013) (0)
On effective σ-boundedness and σ-compactness in Solovay’s model (2015) (0)
Definable Hamel bases and $AC_\omega(R)$ (2019) (0)
The ideal ℐ₃ and the equivalence relation ₃ (2008) (0)
Introduction to countable equivalence relations (2008) (0)
Varia: Ideals and Equivalence Relations, beta-version (2006) (0)
Reasonable non-Radon-Nikodym ideals (2008) (0)
A generic property of Solovay's set $\Sigma$ (2016) (0)
Theories of internal sets (2004) (0)
Ideals and Equivalence Relations, beta-version (2008) (0)
Degrees of subsets of the measurable cardinal in Prikry generic extensions (2007) (0)

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