Tag: set-theory

197 What are some reasonable-sounding statements that are independent of ZFC? 2009-10-22T19:26:48.983

165 Ultrafilters and automorphisms of the complex field 2010-05-09T21:00:21.057

157 Why worry about the axiom of choice? 2010-04-29T02:57:58.080

138 Knuth's intuition that Goldbach might be unprovable 2010-06-11T00:38:40.180

109 Solutions to the Continuum Hypothesis 2010-05-07T07:40:24.337

90 Does every non-empty set admit a group structure (in ZF)? 2010-01-25T21:49:02.497

84 solving $f(f(x))=g(x)$ 2010-03-09T15:40:09.837

73 Does there exist a bijection of $\mathbb{R}^n$ to itself such that the forward map is connected but the inverse is not? 2016-04-11T14:56:13.680

72 Is the analysis as taught in universities in fact the analysis of definable numbers? 2010-10-29T10:47:27.513

68 Proofs of the uncountability of the reals. 2010-11-22T17:19:28.037

66 Does pointwise convergence imply uniform convergence on a large subset? 2010-11-12T04:01:44.457

65 Most 'unintuitive' application of the Axiom of Choice? 2010-04-10T01:21:18.757

64 How do the compact Hausdorff topologies sit in the lattice of all topologies on a set? 2010-02-19T21:09:20.417

63 Succinctly naming big numbers: ZFC versus Busy-Beaver 2010-08-06T00:57:01.217

63 Is every sigma-algebra the Borel algebra of a topology? 2012-02-07T20:40:23.743

61 Logic in mathematics and philosophy 2011-04-20T12:13:02.563

60 Injectivity implies surjectivity 2017-07-04T09:30:14.797

58 What practical applications does set theory have? 2010-01-01T00:34:16.253

55 Inaccessible cardinals and Andrew Wiles's proof 2010-08-16T10:41:32.633

54 Which graphs are Cayley graphs? 2010-02-09T23:14:06.093

53 Set theories without "junk" theorems? 2012-03-10T14:34:19.730

52 Why hasn't mereology succeeded as an alternative to set theory? 2011-03-15T00:47:52.397

52 Forcing as a new chapter of Galois Theory? 2012-06-23T23:43:12.277

51 How should a "working mathematician" think about sets? (ZFC, category theory, urelements) 2016-11-28T17:07:33.487

49 What's wrong with the surreals? 2010-06-24T01:00:12.753

47 Can the symmetric groups on sets of different cardinalities be isomorphic? 2010-01-25T16:06:04.060

47 Non-Borel sets without axiom of choice 2010-07-21T00:09:43.157

46 Arguments against large cardinals 2010-10-29T09:40:13.193

44 Is the ultraproduct concept fundamentally category-theoretic? 2010-01-09T22:12:09.750

44 The origin of sets? 2012-12-22T21:32:43.990

44 Producing finite objects by forcing! 2014-12-15T04:47:22.613

43 Is the non-triviality of the algebraic dual of an infinite-dimensional vector space equivalent to the axiom of choice? 2010-12-14T13:50:45.797

42 When does $A^A=2^A$ without the axiom of choice? 2013-02-24T05:43:15.643

41 A question about ordinal definable real numbers 2010-03-09T14:50:01.063

41 How would one even begin to try to prove that a simple number-theoretic statement is undecidable? 2010-06-11T20:19:26.657

41 Does $2^X=2^Y\Rightarrow |X|=|Y|$ imply the axiom of choice? 2011-11-17T21:42:35.423

40 What the heck is the Continuum Hypothesis doing in Weibel's Homological Algebra? 2011-06-21T21:14:49.823

40 Set-theoretic reformulation of the invariant subspace problem 2013-07-09T05:33:13.580

40 Hilbert's alleged proof of the Continuum Hypothesis in "On the Infinite" 2017-06-12T15:30:39.310

39 Do set-theorists use informal set theory as their meta-theory when talking about models of ZFC? 2016-09-03T17:13:59.927

38 Cardinalities larger than the continuum in areas besides set theory 2010-11-03T17:27:44.693

37 Which topological spaces admit a nonstandard metric? 2010-01-06T02:19:22.757

37 Does an existence of large cardinals have implications in number theory or combinatorics? 2013-05-03T19:35:14.260

37 How many rearrangements must fail to alter the value of a sum before you conclude that none do? 2015-08-13T17:07:26.587

36 Why do categorical foundationalists want to escape set theory? 2010-05-15T16:20:01.893

36 "Simpler" statements equivalent to Con(PA) or Con(ZFC)? 2011-04-24T20:16:29.760

36 Why should we believe in the axiom of regularity? 2015-09-29T18:31:42.450

35 How far is Lindelöf from compactness? 2009-12-23T21:38:41.833

35 What interesting/nontrivial results in Algebraic geometry require the existence of universes? 2010-05-13T23:11:06.747

35 Concerning the various proofs from the axiom of choice that R^3 admits of surprising geometrical decompositions into circles, skew lines and so on: can we prove in any instance that there are no Borel such decompositions? Or that AC is required? 2012-04-09T20:32:24.503

35 Is there a computable ordinal encoding the proof strength of ZF? Is it knowable? 2014-04-23T18:10:36.130

35 Measurability and Axiom of choice 2015-07-14T11:39:29.790

34 Were Bourbaki committed to set-theoretical reductionism? 2010-01-10T08:17:40.680

34 A principle of mathematical induction for partially ordered sets with infima? 2010-09-09T22:51:44.873

34 Is the fixed point property for posets preserved by products? 2014-08-31T14:19:27.040

33 Completion of ZFC 2010-11-22T05:23:55.577

33 Latest stand of core model theory? 2014-01-06T15:23:18.407

33 Chromatic number of a topological space 2018-02-05T14:08:01.133

32 What are interesting families of subsets of a given set? 2009-12-30T07:15:51.263

32 Dual Schroeder-Bernstein theorem 2010-09-15T03:43:19.667

32 Distinct well-orderings of the same set 2010-09-29T18:24:52.950

32 Translates of null sets 2015-02-21T20:40:21.997

32 Bidi: A new cardinal characteristic of the continuum? 2015-05-12T02:27:47.410

31 Do there exist non-PIDs in which every countably generated ideal is principal? 2009-12-06T22:25:52.360

31 What is the general opinion on the Generalized Continuum Hypothesis? 2010-02-06T01:18:48.467

31 On the difference between two concepts of even cardinalities: Is there a model of ZF set theory in which every infinite set can be split into pairs, but not every infinite set can be cut in half? 2011-07-04T12:20:34.080

31 Are there examples of statements that have been proven whose consistency proofs came before their proofs? 2011-07-25T08:08:00.117

31 How large is TREE(3)? 2012-04-12T06:35:54.440

30 Set theory and Model Theory 2010-04-30T01:57:10.443

30 Axiom of Symmetry, aka Freiling's argument against CH 2010-12-17T11:20:06.737

30 What's a magical theorem in logic? 2011-08-29T23:43:16.670

30 Why should we care about "higher infinities" outside of set theory? 2015-08-26T23:54:56.833

30 Is Lagrange's Theorem equivalent to AC? 2016-12-04T01:57:11.810

29 Do sets with positive Lebesgue measure have same cardinality as R? 2009-12-15T10:47:40.713

29 Interpretation of the Second Incompleteness Theorem 2010-09-09T16:28:10.210

29 Clearing misconceptions: Defining "is a model of ZFC" in ZFC 2011-01-11T12:10:47.383

29 The set-theoretic multiverse as a (bi)category 2011-09-19T11:53:46.703

29 Even XOR Odd Infinities? 2013-01-19T23:19:26.353

29 Forcing as a replacement of induction and diagonal arguments 2015-01-07T04:32:46.990

29 Should axiomatic set theory be translated into graph theory? 2016-01-06T08:10:40.483

29 Is it consistent with ZF that $V \to V^{\ast \ast}$ is always an isomorphism? 2018-01-11T14:29:26.680

28 Is "all categorical reasoning formally contradictory"? 2010-05-05T10:16:21.997

28 Understanding the countable ordinals up to $\epsilon_{0}$ 2011-02-20T13:54:48.673

28 What axioms are used to prove Godel's Incompleteness Theorems? 2013-01-06T05:58:18.207

28 Similarities between Post's Problem and Cohen's Forcing 2013-03-08T19:55:21.100

28 What is the fewest number of points you must delete from $\mathbb{R}^3$ to make it not simply connected? 2015-08-31T21:33:34.020

28 Do the analogies between metamathematics of set theory and arithmetic have some deeper meaning? 2015-12-29T14:59:55.753

28 Silver's approach to the inconsistency of $ZFC$ 2017-01-30T17:43:31.660

27 Is there a computable model of ZFC? 2010-01-20T16:38:48.000

27 Can we prove set theory is consistent? 2010-04-26T18:54:01.753

27 Should there be a true model of set theory? 2010-11-06T06:36:26.360

27 Essential reads in the philosophy of mathematics and set theory 2012-04-18T04:15:26.930

27 Continuous functions $f$ with $f(A)$ linearly independent when $A$ is independent 2013-11-18T10:44:27.167

27 Is it possible to define higher cardinal arithmetics 2014-11-24T05:27:42.543

26 How much choice is needed to show that formally real fields can be ordered? 2009-12-11T13:29:00.607

26 Is there a constructive proof of Cantor–Bernstein–Schroeder theorem ? 2013-03-03T17:17:33.240

26 Hahn's Embedding Theorem and the oldest open question in set theory 2013-04-27T17:12:03.140

26 Does every set of reals contain a measure-zero set of the same cardinality? Does it contain a meager set of the same cardinality? 2013-10-10T23:06:10.377

26 Why isn't this a computable description of the ordinal of ZF? 2014-05-06T17:44:31.310