Forcing in Proof Theory Export

@article{citeulike:125876, abstract = {Paul Cohen's method of forcing, together with Saul Kripke's related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will discuss the aspects of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments.}, author = {Avigad, Jeremy}, citeulike-article-id = {125876}, citeulike-linkout-0 = {http://dx.doi.org/10.2307/3185188}, citeulike-linkout-1 = {http://www.jstor.org/stable/3185188}, doi = {10.2307/3185188}, journal = {The Bulletin of Symbolic Logic}, keywords = {constructive, deduction, forcing, intuitionistic, logic, prooftheory}, number = {3}, pages = {305--333}, posted-at = {2005-03-13 03:07:52}, priority = {2}, title = {Forcing in Proof Theory}, url = {http://dx.doi.org/10.2307/3185188}, volume = {10}, year = {2004} }

TY - JOUR ID - citeulike:125876 L3 - citeulike-article-id:125876 N2 - Paul Cohen's method of forcing, together with Saul Kripke's related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will discuss the aspects of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments. IS - 3 JF - The Bulletin of Symbolic Logic EP - 333 TI - Forcing in Proof Theory VL - 10 SP - 305 KW - constructive KW - deduction KW - forcing KW - intuitionistic KW - logic KW - prooftheory AU - Avigad, Jeremy PY - 2004/// UR - http://dx.doi.org/10.2307/3185188 ER -