Results 1 to 10 of about 3,715 (167)

De Jongh’s Theorem for Intuitionistic Zermelo-Fraenkel Set Theory [PDF]

, 2020
We prove that the propositional logic of intuitionistic set theory IZF is intuitionistic propositional logic IPC. More generally, we show that IZF has the de Jongh property with respect to every intermediate logic that is complete with respect to a class
Robert Paßmann
core   +8 more sources

Applying SMT Solvers to the Test Template Framework [PDF]

Electronic Proceedings in Theoretical Computer Science, 2012
The Test Template Framework (TTF) is a model-based testing method for the Z notation. In the TTF, test cases are generated from test specifications, which are predicates written in Z.
Maximiliano Cristiá, Claudia Frydman
doaj   +3 more sources

Normalization of IZF with Replacement [PDF]

Logical Methods in Computer Science, 2008
ZF is a well investigated impredicative constructive version of Zermelo-Fraenkel set theory. Using set terms, we axiomatize IZF with Replacement, which we call \izfr, along with its intensional counterpart \iizfr.
Wojciech Moczydlowski
doaj   +3 more sources

Arrow of Time in Quantum Mechanics and Set Theory [PDF]

Entropy
The set-theory twist of quantum mechanics uncovers forcing in axiomatic Zermelo–Fraenkel set theory as a viable tool to understand the singularities in a physical spacetime and serves as a link between the quantum and classical worlds. The random forcing
Jerzy Król
doaj   +2 more sources

Proof-irrelevant model of CC with predicative induction and judgmental equality [PDF]

Logical Methods in Computer Science, 2011
We present a set-theoretic, proof-irrelevant model for Calculus of Constructions (CC) with predicative induction and judgmental equality in Zermelo-Fraenkel set theory with an axiom for countably many inaccessible cardinals. We use Aczel's trace encoding
Gyesik Lee, Benjamin Werner
doaj   +3 more sources

A Normalizing Intuitionistic Set Theory with Inaccessible Sets [PDF]

Logical Methods in Computer Science, 2007
We propose a set theory strong enough to interpret powerful type theories underlying proof assistants such as LEGO and also possibly Coq, which at the same time enables program extraction from its constructive proofs.
Wojciech Moczydlowski
doaj   +3 more sources

An Easton-like Theorem for Zermelo-Fraenkel Set Theory Without Choice (Preliminary Report) [PDF]

, 2013
By Easton's theorem one can force the exponential function on regular cardinals to take rather arbitrary cardinal values provided monotonicity and Koenig's lemma are respected.
Anne Fernengel, Peter Koepke
openalex   +4 more sources

A program for the full axiom of choice [PDF]

Logical Methods in Computer Science, 2021
The theory of classical realizability is a framework for the Curry-Howard correspondence which enables to associate a program with each proof in Zermelo-Fraenkel set theory.
Jean-Louis Krivine
doaj   +1 more source

Occurence of contradictions in Zermelo-Fraenkel theory under extension of base language by recursion functions [PDF]

Компьютерные исследования и моделирование, 2009
It is shown that the extension of base language in Zermelo-Fraenkel theory, which allows a relations on recursion function of natural argument, may lead in Set Theory to contradictive constructions on arithmetic level.
A. V. Koganov
doaj   +1 more source

Finitely Supported Sets Containing Infinite Uniformly Supported Subsets [PDF]

Electronic Proceedings in Theoretical Computer Science, 2019
The theory of finitely supported algebraic structures represents a reformulation of Zermelo-Fraenkel set theory in which every construction is finitely supported according to the action of a group of permutations of some basic elements named atoms.
Andrei Alexandru, Gabriel Ciobanu
doaj   +1 more source