Literatura k tematu "Gödelovy vety a slozitost " (jaro 2011):
(Postupne bude doplnovano.)
Basics
K.Godel,
Über formal unentscheidbare Sätze der Principia Mathematica
und verwandter Systeme, I. Monatshefte für Mathematik und Physik 38, (19310,
173-98.
English translation.
P.Pudlak,
a chapter from his forthcoming book, 2011.
C.Smorynski,
The incompleteness theorems,
chapter D1 (pp.821-865) in: Handbook of Mathematical Logic, ed.J.Barwise,
Elsevier Science Publishing Co., 1977.
(elektronickou versi dodam)
Longer expositions
Rada standartnich ucebnic logiky ci teorie dukazu podava dukaz Godelovych vet.
Dale tez napr.:
Torkel Franzen,
Godel's Theorem: An Incomplete Guide to Its Use and Abuse,
Taylor&Francis Inc., A K Peters, 2005.
Peter Smith,
An Introduction to Gödel's theorems,
CUP.
2005 preliminary version, and its
pdf.
P.Smith,
Godel without tears, 2011 notes.
Pdf.
Proofs using other paradoxes
These are just rather arbitrary examples:
G.Chaitin,
Computational complexity and Gödel's incompleteness theorem,
ACM SIGACT News, No. 9 (April 1971), pp. 11-12.
Shira Kritchman and Ran Raz,
The Surprise Examination Paradox and the Second Incompleteness Theorem,
Notices AMS, Vol.11, (2010), pp.1454-1458.
Finitistic Godel's theorem
H.Friedman,
On the consistency, completeness and correctness probelms, unpublished manuscript,
Ohio State Univ., 1979.
P. Pudlak:
On the length of proofs of finitistic consistency
statements in first order theories, in: Logic Colloquium 84,
North Holland P.C., 1986 pp.165-196.
P. Pudlak: Improved bounds to the length of proofs of finitistic
consistency statements. In: Contemporary mathematics Vol.65, 1987 pp.309-331.
Links with proof complexity
S.A.Cook,
Feasibly constructive proofs and the propositional calculus ,
Proc. of 7th annual ACM symposium on Theory of computing,
Albuerque, New Mexico, pp.83-97, (1975).
J.Krajicek and P.Pudlak,
Propositional Proof Systems, the Consistency of First
Order Theories and the Complexity of Computations,
J. Symbolic Logic, 54(3), (1989), pp. 1063-1079.
Combinatorial indepence
A.Bovykin,
Brief introduction to unprovability, in: Logic Colloquium 2006,
Lecture Notes in Logic, (2009), pp.38-64.
J.Paris and L.Harrington,
A Mathematical Incompleteness
in Peano Arithmetic,
in: Handbook for Mathematical Logic (Ed. J. Barwise).
Amsterdam, Netherlands: North-Holland, 1977, pp.1133-1142.
Auxiliari
J.Krajicek,
A Note of Proofs of Falsehood,
Archiv f. Mathematikal Logik u. Grundlagen 26 (3-4),
(1987), pp. 169-179.
P. Pudlak,
Cuts, consistency statements and interpretations,
Journ. Symb. Logic Vol.50, 1985, pp.423-441.
Pavel Pudlak,
text
o Feasible incompleteness thesis (sekce 3)
P. Pudlak:
A note on applicability of the incompleteness theorem to human mind,
Annals of Pure and Applied Logic 96 (1999), pp. 335-342