Formative Processes with Applications to the Decision Problem in Set Theory

Domenico Cantone; Pietro Ursino; Eugenio G. Omodeo

doi:10.1006/inco.2001.3096

Formative Processes with Applications to the Decision Problem in Set Theory

Information and Computation ◽

10.1006/inco.2001.3096 ◽

2002 ◽

Vol 172 (2) ◽

pp. 165-201 ◽

Cited By ~ 6

Author(s):

Domenico Cantone ◽

Pietro Ursino ◽

Eugenio G. Omodeo

Keyword(s):

Set Theory ◽

Decision Problem

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Formative processes with applications to the decision problem in set theory: II. Powerset and singleton operators, finiteness predicate

Information and Computation ◽

10.1016/j.ic.2014.02.005 ◽

2014 ◽

Vol 237 ◽

pp. 215-242 ◽

Cited By ~ 1

Author(s):

Domenico Cantone ◽

Pietro Ursino

Keyword(s):

Set Theory ◽

Decision Problem

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Decision procedures for elementary sublanguages of set theory IX. Unsolvability of the decision problem for a restricted subclass of the Δ0-formulas in set theory

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.3160410206 ◽

1988 ◽

Vol 41 (2) ◽

pp. 221-251 ◽

Cited By ~ 19

Author(s):

Franco Parlamento ◽

Alberto Policriti

Keyword(s):

Set Theory ◽

Decision Problem ◽

Decision Procedures

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Effectively retractable theories and degrees of undecidability

Journal of Symbolic Logic ◽

10.2307/2270853 ◽

1970 ◽

Vol 34 (4) ◽

pp. 597-604

Author(s):

J. P. Jones

Keyword(s):

Set Theory ◽

Decision Problem

In this paper a new property of theories, called effective retractability is introduced and used to obtain a characterization for the degrees of subtheories of arithmetic and set theory. By theory we understand theory in standard formalization as defined by Tarski [10]. The word degree refers to the Kleene-Post notion of degree of recursive unsolvability [2]. By the degree of a theory we mean, of course, the degree associated with its decision problem via Gödel numbering.

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