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Truth in the limit

Mostowski M.

Reports on Mathematical Logic

2016

Vol. 51

75--89

We consider sl–semantics in which first order sentences are interpreted in potentially infinite domains. A potentially infinite domain is a growing sequence of finite models. We prove the completeness theorem for first order logic under this semantics. Additionally we characterize the logic of such domains as having a learnable, but not recursive, set of axioms. The work is a part of author’s research devoted to computationally motivated foundations of mathematics.

Potential Infinity and the Church Thesis

Mostowski M.

Fundamenta Informaticae

2007

Vol. 81, nr 1-3

241-248

In this paper we consider a "mathematical" proof of the Church Thesis. The proof is based on very weak assumptions about intuitive computability and the FM-representability theorem from [11]. It develops and improves the argument mentioned in [12]. Our argument essentially depends on the mathematical model of the world we are in.

Finite Arithmetics

Krynicki M., Mostowski M., Zdanowski K.

Fundamenta Informaticae

2007

Vol. 81, nr 1-3

183-202

The paper presents the current state of knowledge in the field of logical investigations of finite arithmetics. This is an attempt to summarize the ideas and results in this area. Some new results are presented - these are mainly generalizations of the earlier results related to properties of sl-theories and some nontrivial cases of FM-representability theorem.