Notre Dame Journal of Formal Logic

Four Problems Concerning Recursively Saturated Models of Arithmetic

Roman Kossak

Abstract

The paper presents four open problems. One concerns a possible converse to Tarski's undefinability of truth theorem, and is of a general character. The other three are more specific. The questions are about some special $\omega_1$-like models, initial segments of countable recursively saturated models of PA, and about extendability of automorphisms. In each case a partial answer is given. All partial solutions are based on applications of inductive satisfaction classes.

Article information

Source
Notre Dame J. Formal Logic, Volume 36, Number 4 (1995), 519-530.

Dates
First available in Project Euclid: 17 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1040136913

Digital Object Identifier
doi:10.1305/ndjfl/1040136913

Mathematical Reviews number (MathSciNet)
MR1368464

Zentralblatt MATH identifier
0848.03016

Subjects
Primary: 03C62: Models of arithmetic and set theory [See also 03Hxx]
Secondary: 03C57: Effective and recursion-theoretic model theory [See also 03D45]

Citation

Kossak, Roman. Four Problems Concerning Recursively Saturated Models of Arithmetic. Notre Dame J. Formal Logic 36 (1995), no. 4, 519--530. doi:10.1305/ndjfl/1040136913. https://projecteuclid.org/euclid.ndjfl/1040136913


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