Four problems concerning recursively saturated models of arithmetic. (English) Zbl 0848.03016

Kossak, Roman

Notre Dame J. Formal Logic 36, No. 4, 519-530 (1995).

The paper presents four open problems. One concerns a possible converse to Tarski’s undefinability of truth theorem, and is of 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.

Reviewer: R.Kossak (New York)

MSC:

03C62	Models of arithmetic and set theory
03C50	Models with special properties (saturated, rigid, etc.)

Keywords:

Peano arithmetic; recursive saturation; open problems; recursively saturated models of PA; extendability of automorphisms; inductive satisfaction classes

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