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CORR
2004
Springer
176views Education» more  CORR 2004»
13 years 7 months ago
The First-Order Theory of Sets with Cardinality Constraints is Decidable
Data structures often use an integer variable to keep track of the number of elements they store. An invariant of such data structure is that the value of the integer variable is ...
Viktor Kuncak, Martin C. Rinard
ITP
2010
165views Mathematics» more  ITP 2010»
13 years 11 months ago
A Mechanized Translation from Higher-Order Logic to Set Theory
Abstract. In order to make existing formalizations available for settheoretic developments, we present an automated translation of theories from Isabelle/HOL to Isabelle/ZF. This c...
Alexander Krauss, Andreas Schropp
APAL
2004
132views more  APAL 2004»
13 years 7 months ago
Canonical structure in the universe of set theory: part one
Abstract. We start by studying the relationship between two invariants isolated by Shelah, the sets of good and approachable points. As part of our study of these invariants, we pr...
James Cummings, Matthew Foreman, Menachem Magidor
LICS
1999
IEEE
14 years 2 days ago
First-Order Logic vs. Fixed-Point Logic in Finite Set Theory
The ordered conjecture states that least fixed-point logic LFP is strictly more expressive than first-order logic FO on every infinite class of ordered finite structures. It has b...
Albert Atserias, Phokion G. Kolaitis
CORR
2008
Springer
103views Education» more  CORR 2008»
13 years 8 months ago
Executable Set Theory and Arithmetic Encodings in Prolog
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic...
Paul Tarau