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On a problem of H. Friedman and its solution by T. Prucnal

Wojtylak P.

Reports on Mathematical Logic

2004

Nr 38

69-86

Prucnal proved, see [8] and [9], that Medvedev's logic ML of finite problems is structurally complete. So far, ML is the only known structurally complete intermediate logic with the disjunction property. Another proof of Prucnal's theorem was given by D. Skvortsov [10]. We refresh Prucnal's original argument and prove that all structurally complete intermediate logics with the disjunction property coincide on monadic formulas. The logic are also provided with appropriate Kripke frames.

On the problem of R. E. Tax

Wojtylak P., Wroński A.

Reports on Mathematical Logic

2001

No. 35

87-101

We prove that the purely equivalential fragment of intuitionic logic is not axiomatizable by a finite number of axiom schemata and the modus ponens rule for equivalence as the only rule of inference.

The Sum Operation and Llink Lattices

Grygiel J., Wojtylak P.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

1999

Vol. 6

23--28

The sum operation, as introduced by Andrzej Wroński, is used to decompose any finite distributive lattice into its Boolean fragments. The decomposition is not unique but its maximal components are uniquely determined. We define an ordering relation between these maximal Boolean fragments of a given lattice and use this link ordering to describe the structure of the lattice.