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Wikipedia surprisingly does not contain a good list. Under philosophy of mathematics it is rather vacant too. A graduate level list is here, but I was curious more about the most influential papers. Manually one could search here. But all in all, the database out there is rather barren.

Edit: For some reason when I was typing the title it did not suggest me this math.SE question. (will delete if duplicate).

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What sort of logic are you interested in? The papers in the list you linked to are mostly classical computability theory. – Alex Becker May 11 '12 at 5:38
Well, there is "Mathematical logic in the 20th century", A collection of 31 landmark papers. It is an excellent selection. – Andrés E. Caicedo May 11 '12 at 5:40
Alex, I am more interested in the influential papers from any arena here although the danger in a subjective list. – Sniper Clown May 11 '12 at 5:43
@AndresCaicedo Thank you. I was wondering if the list is manually extracted as an answer, will it be easier for spiders to siphon them in wiki list? – Sniper Clown May 11 '12 at 5:46
The Undecidable (Dover Publications) ed. Martin Davis is a collection of English translations of influential papers by Godel, Church, Turing, Rosser, Kleene and Post on undecidability, incompleteness, computability and so on. Davis writes helpful introductions too - it's well worth a look if you're interested in that sort of thing. – m_t_ May 11 '12 at 7:23
up vote 7 down vote accepted

All these lists are bound to be incomplete and more subjective than one would like, but a truly excellent selection of landmark papers can be found in the book "Mathematical logic in the 20th century", edited by Gerald Sacks, World Scientific, 2003.

Here is the table of contents:

  1. The Independence of the Continuum Hypothesis. Cohen, Paul J.
  2. The Independence of the Continuum Hypothesis II. Cohen, Paul J.
  3. Marginalia to a Theorem of Silver. Devlin, K. I. and Jensen, R. B.
  4. Three Theorems on Recursive Enumeration. I. Decomposition. II. Maximal Set. III. Enumeration without Duplication. Friedberg, Richard M.
  5. Higher Set Theory and Mathematical Practice. Friedman, Harvey M.
  6. Introduction to $\Pi^1_2$-Logic. Girard, Jean-Yves.
  7. Consistency-Proof for the Generalized Continuum-Hypothesis. Gödel, Kurt.
  8. The Mordell-Lang Conjecture for Function Fields. Hrushovski, Ehud.
  9. Model-Theoretic Invariants: Applications to Recursive and Hyperarithmetic Operations. Kreisel, G.
  10. Recursive Functionals and Quantifiers of Finite Types I. Kleene, S. C.
  11. A Recursively Enumerable Degree which will not Split over all Lesser Ones. Lachlan, A. H.
  12. Measurable Cardinals and Analytic Games. Martin, Donald A.
  13. Enumerable Sets are Diophantine. Matijasevic, Ju. V.
  14. Categoricity in Power. Morley, Michael.
  15. Hyperanalytic Predicates. Moschovakis, Y. N.
  16. Solution of Post's Reduction Problem and Some Other Problems of the Theory of Algorithms. Muchnik, A. A.
  17. Recursively Enumerable Sets of Positive Integers and Their Decision Problems. Post, Emil L.
  18. Non-Standard Analysis. Robinson, Abraham.
  19. The Recursively Enumerable Degrees are Dense. Sacks, Gerald E.
  20. Measurable Cardinals and Constructible Sets. Scott, Dana.
  21. Stable Theories. Shelah, S.
  22. The Problem of Predicativity. Shoenfield, J. R.
  23. On the Singular Cardinals Problem. Silver, Jack.
  24. Automorphisms of the Lattice of Recursively Enumerable Sets. Part I: Maximal Sets. Soare, Robert
  25. A Model of Set-Theory in which Every Set of Reals is Lebesgue Measurable. Solovay, Robert M.
  26. On Degrees of Recursive Unsolvability. Spector, Clifford.
  27. A Decision Method for Elementary Algebra and Geometry. Tarski, Alfred.
  28. Denumerable Models of Complete Theories. Vaught, R. L.
  29. Model Completeness Results for Expansions of the Ordered Field of Real Numbers by Restricted Pfaffian Functions and the Exponential Function. Wilkie, A. J.
  30. Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees. Woodin, W. Hugh.
  31. Structural Properties of Models of $\aleph_1$-Categorical Theories. Zil'ber, B. I.

(Full bibliographical details for each paper can be found in the book, of course.)

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Thank you. Enough to keep me busy for 31 days...barring the price when purchasing the papers. – Sniper Clown May 11 '12 at 6:30
It's probably worth pointing out that this is a slightly misleading list when it comes to "most important and influential publicatins", since almost all of them are from after the Second World War (Gödel's paper is from 1938 and Tarski's, while from 1948, is based on results he obtained much earlier), while many of the most important advances in logic date from the 1930s. – Benedict Eastaugh May 11 '12 at 7:32

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