# Andreas Blass

Mathematician

## Andreas Blass's AcademicInfluence.com Rankings

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Mathematics

## Why Is Andreas Blass Influential?

(Suggest an Edit or Addition)According to Wikipedia, Andreas Raphael Blass is a mathematician, currently a professor at the University of Michigan. He works in mathematical logic, particularly set theory, and theoretical computer science. Blass graduated from the University of Detroit, where he was a Putnam Fellow in 1965, in 1966 with a B.S. in physics. He received his Ph.D. in 1970 from Harvard University, with a thesis on Orderings of Ultrafilters written under the supervision of Frank Wattenberg. Since 1970 he has been employed by the University of Michigan, first as a T.H. Hildebrandt Research Instructor , then assistant professor , associate professor and since 1984 he has been a full professor there.

## Andreas Blass's Published Works

### Published Works

- Annals of Pure and Applied Logic (1991) (1549)
- Combinatorial Cardinal Characteristics of the Continuum (2010) (476)
- A Game Semantics for Linear Logic (1992) (320)
- Abstract state machines capture parallel algorithms (2003) (181)
- On the Unique Satisfiability Problem (1982) (139)
- Choiceless Polynomial Time (1997) (119)
- There may be simple Paleph1 and Paleph2-points and the Rudin-Keisler ordering may be downward directed (1987) (118)
- Henkin quantifiers and complete problems (1986) (106)
- Properties of almost all graphs and complexes (1979) (106)
- Algorithms: A Quest for Absolute Definitions (2003) (95)
- A Zero-One Law for Logic with a Fixed-Point Operator (1986) (82)
- The Rudin-Keisler ordering of $P$-points (1973) (74)
- Partition Theorems for Spaces of Variable Words (1994) (74)
- Ultrafilters with small generating sets (1989) (68)
- Mobius functions of lattices (1997) (68)
- Injectivity, projectivity, and the axiom of choice (1979) (66)
- A partition theorem for perfect sets (1981) (66)
- Paley graphs satisfy all first-order adjacency axioms (1981) (65)
- Consistency results about filters and the number of inequivalent growth types (1989) (65)
- Near coherence of filters. II. Applications to operator ideals, the Stone-Čech remainder of a half-line, order ideals of sequences, and slenderness of groups (1987) (64)
- On polynomial time computation over unordered structures (2001) (63)
- Near coherence of filters. I. Cofinal equivalence of models of arithmetic (1986) (62)
- Applications of superperfect forcing and its relatives (1989) (61)
- When are Two Algorithms the Same? (2008) (61)
- Content-dependent chunking for differential compression, the local maximum approach (2010) (60)
- Existential Fixed-Point Logic (1987) (58)
- Cardinal Characteristics and the Product of Countably Many Infinite Cyclic Groups (1992) (57)
- Abstract state machines capture parallel algorithms: Correction and extension (2006) (55)
- Logical analysis of some theorems of combinatorics and topological dynamics (1987) (55)
- Background, Reserve, and Gandy Machines (2000) (53)
- Degrees of indeterminacy of games (1972) (53)
- Selective ultrafilters and homogeneity (1988) (52)
- Ordinary interactive small-step algorithms, I (2007) (51)
- Near Coherence of Filters III: A Simplified Consistency Proof (1989) (51)
- On strongly summable ultrafilters and union ultrafilters (1987) (49)
- Existence of bases implies the axiom of choice (1984) (48)
- The Logic of Choice (2000) (45)
- Characteristic and Ehrhart Polynomials (1998) (44)
- Equivalence Relations, Invariants, and Normal Forms (1983) (43)
- Infinitary combinatorics and modal logic (1990) (43)
- Inadequacy of computable loop invariants (2001) (43)
- Ultrafilters: Where topological dynamics = algebra = combinatorics (1993) (43)
- THE DESCRIPTIVE SET THEORY OF POLISH GROUP ACTIONS (LMS Lecture Note Series 232) By Howard Becker and Alexander S. Kechris: 136 pp., £21.95 (LMS Members' price £16.45), ISBN 0 521 57605 9 (Cambridge University Press, 1996). (1998) (42)
- Play to Test (2005) (40)
- Interactive Small-Step Algorithms II: Abstract State Machines and the Characterization Theorem (2007) (39)
- Ramsey's theorem in the hierarchy of choice principles (1977) (37)
- Ultrafilter mappings and their dedekind cuts (1974) (37)
- Matrix Transformation Is Complete for the Average Case (1995) (35)
- Questions and answers: a category arising in linear logic complexity theory, and set theory (1993) (35)
- Program termination and well partial orderings (2008) (34)
- Interactive Small-Step Algorithms I: Axiomatization (2007) (33)
- Graphs with unique maximal clumpings (1978) (30)
- On the cofinality of ultrapowers (1996) (29)
- Simple Cardinal Characteristics of the Continuum (1994) (28)
- Freyd's models for the independence of the axiom of choice (1989) (28)
- Seven trees in one (1994) (27)
- Randomizing Reductions of Search Problems (1991) (26)
- A note on extensions of asymptotic density (2001) (25)
- Which trees are link graphs? (1980) (25)
- Bijective proofs of two broken circuit theorems (1986) (25)
- A Model-Theoretic View of Some Special Ultrafilters (1978) (25)
- Reductions Between Cardinal Characteristics of the Continuum (1994) (25)
- Classifying topoi and finite forcing (1983) (24)
- Complexity of winning strategies (1972) (24)
- Pairwise Testing (2002) (23)
- Fields of Logic and Computation (2011) (23)
- Two closed categories of filters (1977) (23)
- Equivalence of two strong forms of determinacy (1975) (23)
- THE NEXT BEST THING TO A P-POINT (2013) (23)
- Abstract State Machines and Computationally Complete Query Languages (2000) (22)
- Groupwise density and related cardinals (1990) (22)
- Prime ideals yield almost maximal ideals (1987) (21)
- The Linear Time Hierarchy Theorems for Abstract State Machines and RAMs (2017) (20)
- Quasi-selective ultrafilters and asymptotic numerosities (2010) (19)
- Strong extension axioms and Shelah's zero-one law for choiceless polynomial time (2003) (18)
- The Underlying Logic of Hoare Logic (2001) (18)
- A characterization and sum decomposition for operator ideals (1978) (18)
- An application of universal algebra in group theory. (1974) (17)
- General Interactive Small Step Algorithms (2005) (17)
- Fields of Logic and Computation II (2015) (17)
- Exact Exploration and Hanging Algorithms (2010) (17)
- Some Semantical Aspects of Linear Logic (1997) (17)
- Words, free algebras, and coequalizers (1983) (17)
- Evidential Authorization (2010) (16)
- Amalgamation of nonstandard models of arithmetic (1977) (15)
- Ultrafilters across Mathematics (2010) (15)
- The intersection of nonstandard models of arithmetic (1972) (15)
- Background of Computation (2007) (15)
- Subgroups of the Baer–Specker group with few endomorphisms but large dual (1994) (14)
- Some Abelian Groups with Free Duals (1995) (14)
- Algorithms vs. Machines (2002) (14)
- Ordinary interactive small-step algorithms, II (2007) (14)
- Finite Embeddability of Sets and Ultrafilters (2014) (14)
- Cohomology detects failures of the axiom of choice (1983) (14)
- Exact functors and measurable cardinals. (1976) (14)
- On the Reduction Theory for Average Case Complexity (1990) (13)
- The model of set theory generated by countably many generic reals (1981) (13)
- Ordinary interactive small-step algorithms, III (2007) (13)
- An axiomatic approach to rank in model theory (1974) (13)
- End extensions, conservative extensions, and the Rudin-Frolík ordering (1977) (13)
- Optimal ancilla-free Pauli+V circuits for axial rotations (2014) (13)
- On strong P-points (2013) (13)
- Modular difference logic is hard (2008) (12)
- SOME QUESTIONS ARISING FROM HINDMAN'S THEOREM (2005) (12)
- Topoi and Computation (1993) (12)
- The Number of Near-Coherence Classes of Ultrafilters is Either Finite or 2 c (2005) (11)
- On certain types and models for arithmetic (1974) (10)
- Fields of Logic and Computation III: Essays Dedicated to Yuri Gurevich on the Occasion of His 80th Birthday (2020) (10)
- Inaccessible cardinals without the axiom of choice (2003) (10)
- Advances in Linear Logic: A category arising in linear logic, complexity theory and set theory (1995) (10)
- The rearrangement number (2016) (10)
- Homogeneous sets from several ultrafilters (2009) (9)
- Is Game Semantics Necessary? (1993) (9)
- Addendum to "Choiceless Polynomial Time": Ann. Pure Appl. Logic 100 (1999) 141-187 (2001) (9)
- Kleene degrees of ultrafilters (1985) (9)
- Evolving Algebras and Linear Time Hierarchy (1994) (9)
- A Note on Nested Words (2006) (8)
- Weak partition relations (1972) (8)
- A New Zero-One Law and Strong Extension Axioms (2000) (8)
- Explicit Graphs with Extension Properties (2005) (8)
- Specker’s theorem for Nöbeling’s group (2001) (8)
- Needed reals and recursion in generic reals (2001) (7)
- Complete Topoi Representing Models of Set Theory (1992) (7)
- Partitions and Permutation Groups (2009) (7)
- Persistent queries in the behavioral theory of algorithms (2011) (7)
- Why Sets? (2008) (7)
- Two Forms of One Useful Logic: Existential Fixed Point Logic and Liberal Datalog (2008) (7)
- Hilbertian Deductive Systems, Infon Logic, and Datalog (2013) (6)
- On Matijasevitch's Nontraditional Approach to Search Problems (1989) (6)
- Negative probabilities, II What they are and what they are for (2018) (6)
- Some initial segments of the Rudin-Keisler ordering (1981) (6)
- Natural endomorphisms of Burnside rings (1979) (5)
- Boolean classifying topoi (1983) (5)
- On Quantum Computation, Anyons, and Categories (2015) (5)
- Propositional connectives and the set theory of the continuum (1996) (5)
- FREE SUBGROUPS OF THE BAER-SPECKER GROUP (2001) (5)
- Mm Obius Functions of Lattices (1995) (5)
- An introduction to DKAL (2012) (5)
- FREE SUBGROUPS OF THE HOMEOMORPHISM GROUP OF THE REALS (1986) (5)
- There are not exactly five objects (1984) (4)
- Witness algebra and anyon braiding (2018) (4)
- A Faithful Modal Interpretation of Propositional Ontology (2004) (4)
- A Faithful Modal Interpretation of Propositional Ontology (2004) (4)
- Abstract State Machines and Pure Mathematics (2000) (4)
- Generalizing Hartogs' Trichotomy Theorem (2008) (4)
- Exact Exploration (2009) (4)
- On the Egoroff property of pointwise convergent sequences of functions (1986) (4)
- Conservative extensions of models of arithmetic (1980) (4)
- Determinateness and continuity (1973) (4)
- Circuit pedantry (2019) (4)
- Review: D. J. Shoesmith and T. J. Smiley, Multiple-conclusion logic (1980) (3)
- Contemporary Mathematics Partitions and Permutation Groups (2011) (3)
- Review: Martin Davis, Applied nonstandard analysis, and K. D. Stroyan and W. A. J. Luxemburg, Introduction to the theory of infinitesimals, and H. Jerome Keisler, Foundations of infinitesimal calculus (1978) (3)
- Homotopy and Homology of Finite Lattices (2003) (3)
- Basic Subgroups and Freeness, a Counterexample (2007) (3)
- Cores of $\Pi^1_1$ Sets of Reals (1974) (3)
- Quantum circuits with classical channels and the principle of deferred measurements (2021) (3)
- Purity and Reid’s theorem (1999) (3)
- Symbioses between mathematical logic and computer science (2016) (3)
- Circuits: An abstract viewpoint (2020) (3)
- Spekkens's Symmetric No-Go Theorem (2015) (3)
- Cores of Π1 1 sets of reals (1974) (3)
- The Number of Near-Coherence Classes of Ultrafilters is Either Finite or \( 2^\mathfrak{c} \) (2006) (3)
- Persistent Queries (2008) (3)
- Ultrafilters and Partial Products of Infinite Cyclic Groups (2005) (3)
- The Tower-of-Babel Problem, and Security Assesment Sharing (2010) (3)
- Negative probabilities: what are they for? (2021) (3)
- Small decidable sheaves (1986) (2)
- Optimal no-go theorem on hidden-variable predictions of effect expectations (2018) (2)
- Abstract Hilbertian deductive systems, infon logic, and Datalog (2013) (2)
- Basic subgroups and a freeness criterion for torsion-free abelian groups (1999) (2)
- Existential Fixed-Point Logic, Universal Quantifiers, and Topoi (2010) (2)
- Zero-One Laws: Thesauri and Parametric Conditions (2007) (2)
- Coherence for braided distributivity (2018) (2)
- A Course in Universal Algebra. By Stanley Burris and H. P. Sankappanavar (1984) (2)
- Review: Marcia J. Groszek, Applications of Iterated Perfect Set Forcing (1990) (2)
- Disjoint Non-Free Subgoups of Abelian Groups (2005) (2)
- A Quick Update on the Open Problems in Blass-Gurevich-Shelah's article \On Polynomial Time Computations Over Unordered Structures" (2017) (2)
- Random Orders and Gambler's Ruin (2005) (2)
- Ancilla-approximable quantum state transformations (2014) (2)
- 2003 Annual Meeting of the Association for Symbolic Logic (2004) (2)
- A Variation on the Zero-One Law (1998) (2)
- A forcing proof of the Kechris-Moschovakis constructibility theorem (1975) (2)
- One Useful Logic That Defines Its Own Truth (2008) (2)
- Choiceless Polynominal Time Computation and the Zero-One Law (2000) (2)
- Functions on universal algebras (1986) (2)
- Corrections to: “Exact functors and measurable cardinals” (1977) (1)
- On the divisible parts of quotient groups (1993) (1)
- Axioms and Models for an Extended Set Theory (2012) (1)
- Fixed-Choice and Independent-Choice Logics (1998) (1)
- The Logic in Computer Science Column the Underlying Logic of Hoare Logic (2001) (1)
- Degree Sequences of Infinite Graphs (1981) (1)
- Special Families of Sets and Baer-Specker Groups (2005) (1)
- Common Denominator for Value and Expectation No-go Theorems: Extended Abstract (2017) (1)
- Divisibility of Dedekind finite Sets (2005) (1)
- Theories without countable models (1972) (1)
- Diverse Homogeneous Sets (1992) (1)
- Why Sets? (Column: Logic in Computer Science) (2004) (1)
- On exponentiation of G-sets (1994) (1)
- An Invitation to Quantum Computing (2018) (1)
- Acknowledgement of priority (1985) (1)
- Quasi-Varieties, Congruences, and Generalized Dowling Lattices (1995) (1)
- ULTRAFILTERS AND CARDINAL CHARACTERISTICS OF THE CONTINUUM (2015) (1)
- An induction principle and pigeonhole principles for K-finite sets (1994) (1)
- On the Rectilinear Steiner Problem (2017) (1)
- Simple circuit simulations of classical and quantum Turing machines (2021) (1)
- Who needs category theory? (2018) (1)
- Partitions and conservativity (2015) (1)
- THE LOGIC IN COMPUTER SCIENCE COLUMN by Yuri GUREVICH Algorithms vs. Machines (2002) (0)
- On The Confinality of Ultrapowers (1999) (0)
- Howard Paul and Rubin Jean E.. Consequences of the axiom of choice, Mathematical Surveys and Monographs, vol. 59. American Mathematical Society, Providence, RI, 1998, viii + 432 pp. (2005) (0)
- Review: W. W. Comfort, S. Negrepontis, The Theory of Ultrafilters (1976) (0)
- Software science view on quantum circuit algorithms (2022) (0)
- AND UNI()N ULTRiFILTERS (2016) (0)
- Exact functors, local connectedness and measurable cardinals (1985) (0)
- A NON-HOMOGENEITY PROPERTY OF rj-IDEALS (2010) (0)
- Quantum circuits computing unitary transformations (2021) (0)
- T L C S C B C (2007) (0)
- VOTING RULES FOR INFINITE SETS AND BOOLEAN ALGEBRAS (2006) (0)
- Yuri, Logic, and Computer Science (2010) (0)
- Introduction to Secret-Sharing (2016) (0)
- A Note on Idempotents in Banach Algebras (1971) (0)
- SHARED SECRETS (2021) (0)
- ON THE DIVISIBLE PARTS OF QUOTIENT GROUPSAndreas BlassAbstract (2007) (0)
- XI’I’Y OF WINNING STRATEGIES (2001) (0)
- ORDERINGS WITH lTH JUMP DEGREE 0(a) (2016) (0)
- Association for Symbolic Logic (1991) (0)
- Adapting Logics (2006) (0)
- Cores of pi11 Sets of Reals (1974) (0)
- Rewrite plan for my research monograph (0)
- C ircuits : A n abstract viewpoint (2020) (0)
- Input Independence (2021) (0)
- Functional Thesauri, Classifying Topoi, Unification, and Flatness (2020) (0)
- GRAPH COLORINGS (2018) (0)
- Meeting of the Association for Symbolic Logic, East Lansing, Michigan, 1988 (1989) (0)
- L O ] 3 0 Ju l 2 01 8 WHO NEEDS CATEGORY THEORY ? (0)
- REVIEWS-Consequences of the axiom of choice (2005) (0)
- L O ] 1 2 Ju l 1 99 4 REDUCTIONS BETWEEN CARDINAL CHARACTERISTICS OF THE CONTINUUM (1996) (0)
- On a problem of H. N. Gupta (1996) (0)
- T L C S C T F O U L: E F P L L D (2008) (0)
- Meeting of the Association for Symbolic Logic, Chicago, 1985 (1986) (0)
- Sperner spaces and first‐order logic (2003) (0)
- Is There a Core Class for Almost Free Groups of Size ℵ 1 ? (2004) (0)
- Mo bius Functions of Lattices (1997) (0)
- CLASSIFYING TOP 01 AND FINITE FORCING (2001) (0)
- Makkai Michael and Paré Robert. Accessible categories: the foundations of categorical model theory . Contemporary mathematics, vol. 104. American Mathematical Society, Providence 1989, viii + 176 pp. (1993) (0)
- INTERPRETING EXTENDED SET THEORY IN CLASSICAL SET THEORY (2010) (0)
- NP-Completeness of Deciding Binary Genetic Encodability (2005) (0)
- Surveyable sets (2018) (0)
- O n the rectilinear S teiner problem (2017) (0)
- Equivalence relations, invariants, and normal functions (1982) (0)
- THE AXIOM OF CHOICE (2009) (0)
- Gainesville, Florida March 10–13, 2007 (2007) (0)
- Generating Strategies from Transient Test Graphs ⋆ (2004) (0)
- On the Number of Near-Coherence Classes of Ultrafilters (2004) (0)
- On the Cofinality of Ultrapowers Author(s): (2007) (0)
- Theory and Application of Abstract State Machines (Dagstuhl Seminar 02101) (2021) (0)
- On the inadequacy of inner models (1972) (0)
- Braided distributivity. (2019) (0)
- Infinitary Partition Properties of Sums of Selective Ultrafilters (2020) (0)
- Composants of the Stone–Čech remainder of the reals (2015) (0)
- Wigner's quasidistribution and Dirac's kets (2022) (0)
- Book Review: Applied nonstandard analysis@@@Book Review: Introduction to the theory of infinitesimals@@@Book Review: Foundations of infinitesimal calculus (1978) (0)
- About books (1982) (0)
- 0 Ju l 2 01 5 ON QUANTUM COMPUTATION , ANYONS , AND CATEGORIES (0)
- New Orleans Marriott and Sheraton New Orleans Hotels New Orleans, LA January 8–9, 2011 (2012) (0)
- Developments from Ernst Specker’s Work in Set Theory (2012) (0)
- Baire category for monotone sets (1994) (0)
- Existential Fixed-Point Logic as a Fragment of Second-Order Logic (2015) (0)
- Classifying topoi and the axiom of infinity (1989) (0)
- THE LOGIC IN COMPUTER SCIENCE COLUMN by Yuri GUREVICH Pairwise Testing (2002) (0)

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