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LOGICAL FRAMEWORKS FOR TRUTH AND ABSTRACTION SL 135
This English translation of the author's original work has been thoroughly revised, expanded and updated.
The book covers logical systems known as
Research arising from paradoxes has moved progressively closer to the mainstream of mathematical logic and has become much more prominent in the last twenty years. A number of significant developments, techniques and results have been discovered.
Academics, students and researchers will find that the book contains a thorough overview of all relevant research in this field.
Preface. Contents. Introduction. PART A: COMBINATORS AND TRUTH. I. Introducing operations. II. Extending operations with reflective truth. PART B: TRUTH AND RECURSION THEORY. III. Inductive models and definability theory. IV. Type-free abstraction with approximation operator. V. Type-free abstraction, choice and sets. PART C: SELECTED TOPICS. VI. Levels of implication and intentional logical equivalence. VII. On the global structure of models for reflective truth. PART D: LEVELS OF TRUTH AND PROOF THEORY. VIII. Levels of reflective truth. IX. Levels of truth and predicative well-orderings. X. Reducing reflective truth with levels to finitely iterated reflective truth. XI. Proof-theoretic investigation of finitely iterated reflective truth. PART E: ALTERNATIVE VIEWS. XII. Non-reductive systems for type-free abstraction and truth. XIII. The variety of non-reductive approaches. XIV. Epilogue: applications and perspectives. Bibliography. Index. List of Symbols. Series: Studies in Logic and the Foundations of Mathematics