Foundational Studies Selected Works (eBook)

Front Cover 1
Foundational Studies: Selected Works 5
Copyright Page 6
Contents 7
Editorial note 9
A. Mostowski (1913–1975) 11
Bibliography of works of A. Mostowski 13
Andrzej Mostowski's studies of decidability, recursion and hierarchy 23
The investigations of Andrzej Mostowski in the foundations of set theory 29
The work of Andrzej Mostowski in model theory 35
Research work of A. Mostowski in logical calculi 43
Contribution of Mostowski to foundation of second order arithmetic 47
Chapter 1 Thirty years of foundational studies 49
Chapter 2 Models of set theory 225
Chapter 3 On the independence of the well-ordering theorem from the ordering principle 338
Chapter 4 On definable sets of positive integers 387
Chapter 5 The classical and the .-complete arithmetic 419
Chapter 6 Formal system of analysis based on an infinitistic rule of proof 438
Chapter 7 An exposition of forcing 464
Chapter 8 Some impredicative definitions in the axiomatic set-theory 527
Chapter 9 Models of axiomatic theories admitting automorphisms 542
Chapter 10 On .-models which are not ß-models 561
Chapter 11 Observations concerning elementary extensions of .-models I 572
Chapter 12 An undecidable arithmetical statement 579
Chapter 13 On extendability of models of ZF set theory to the models of Kelley–Morse theory of classes 601