Tekijä: Helmut Schwichtenberg; Stanley S. Wainer Kustantaja: Cambridge University Press (2011) Saatavuus: | Arvioimme, että tuote lähetetään meiltä noin 1-3 viikossa
Tekijä: Friedrich L. Bauer; Wilfried Brauer; Helmut Schwichtenberg Kustantaja: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG (1993) Saatavuus: Noin 17-20 arkipäivää
Tekijä: Klaus Mainzer; Peter Michael Schuster; Helmut Schwichtenberg Kustantaja: World Scientific Publishing Co Pte Ltd (2018) Saatavuus: Noin 16-19 arkipäivää
Tekijä: Douglas Bridges; Hajime Ishihara; Michael Rathjen; Helmut Schwichtenberg Kustantaja: Cambridge University Press (2023) Saatavuus: | Arvioimme, että tuote lähetetään meiltä noin 1-3 viikossa
Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
