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Grzegorczyk’s Logics. Part I

100%
Huuskonen T.
Formalized Mathematics
|
2015
|
tom 23
|
nr 3
177-187
EN
This article is the second in a series formalizing some results in my joint work with Prof. Joanna Golinska-Pilarek ([9] and [10]) concerning a logic proposed by Prof. Andrzej Grzegorczyk ([11]). This part presents the syntax and axioms of Grzegorczyk’s Logic of Descriptions (LD) as originally proposed by him, as well as some theorems not depending on any semantic constructions. There are both some clear similarities and fundamental differences between LD and the non-Fregean logics introduced by Roman Suszko in [15]. In particular, we were inspired by Suszko’s semantics for his non-Fregean logic SCI, presented in [16].
2
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Polish Notation

100%
Huuskonen T.
Formalized Mathematics
|
2015
|
tom 23
|
nr 3
161-176
EN
This article is the first in a series formalizing some results in my joint work with Prof. Joanna Golinska-Pilarek ([12] and [13]) concerning a logic proposed by Prof. Andrzej Grzegorczyk ([14]). We present some mathematical folklore about representing formulas in “Polish notation”, that is, with operators of fixed arity prepended to their arguments. This notation, which was published by Jan Łukasiewicz in [15], eliminates the need for parentheses and is generally well suited for rigorous reasoning about syntactic properties of formulas.
3
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Hyers-Ulam constants of Hilbert spaces

63%
Huuskonen T., Väısälä J.
Studia Mathematica
|
2002
|
tom 153
|
nr 1
31-40
EN
The best constant in the Hyers-Ulam theorem on isometric approximation in Hilbert spaces is equal to the Jung constant of the space.
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