6533b82ffe1ef96bd12964e3

RESEARCH PRODUCT

Rasiowa–Sikorski Sets and Forcing

Janusz Czelakowski

subject

Set (abstract data type)Pure mathematicsPerspective (geometry)Forcing (recursion theory)Countable setIsomorphismMathematics

description

The paper is concerned with the problem of building models for first-order languages from the perspective of the classic paper of Rasiowa and Sikorski (1950). The central idea, due to Rasiowa and Sikorski and developed in this paper, is constructing first-order models from individual variables. The notion of a Rasiowa–Sikorski set of formulas of an arbitrary language L is introduced. Investigations are confined to countable languages. Each Rasiowa–Sikorski set defines a countable model for L. Conversely, each countable model for L is determined, up to isomorphism, by some Rasiowa–Sikorski set. Consequences of these facts are investigated.

yearjournalcountryeditionlanguage
2018-01-01
https://doi.org/10.1007/978-3-319-69917-2_7