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OP-10067Logic and foundationsStatus unassessed

Erdős #1220 · set theory / ramsey theory

Let lambda be a singular cardinal such that both lambda and mathrm cf ( lambda) are aleph 0 -inaccessible. Does lambda to ( lambda, aleph 1)^2 hold?

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9413Logic and foundationsOpen

Erdős #1218 · set theory / ramsey theory

Assume the Generalised Continuum Hypothesis and let beta= omega omega+1 . Is it true that aleph beta+1 not to ( aleph beta,4, ldots,4)^3 (where there are countably infinite many copies of 4 )?

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9390Logic and foundationsOpen

Erdős #1177 · set theory / chromatic number

Let G be a finite 3 -uniform hypergraph, and let F G( kappa) denote the collection of 3 -uniform hypergraphs with chromatic number kappa not containing G . If F G( aleph 1) is not empty then there exists $X …

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9389Logic and foundationsOpen

Erdős #1175 · set theory / chromatic number

Let kappa be an uncountable cardinal. Must there exist a cardinal lambda such that every graph with chromatic number lambda contains a triangle-free subgraph with chromatic number kappa ?

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9388Logic and foundationsOpen

Erdős #1173 · set theory / combinatorics

Assume the generalised continuum hypothesis. Let f: omega omega+1 to [ omega omega+1 ]^ leq aleph omega be a set mapping such that lvert f( alpha) cap f( beta) rvert < aleph omega for all $ al…

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9387Logic and foundationsOpen

Erdős #1172 · set theory / ramsey theory

Establish whether the following are true assuming the generalised continuum hypothesis: omega 3 to ( omega 2, omega 1+2)^2, omega 3 to ( omega 2+ omega 1, omega 2+ omega)^2, omega 2 to ( omega 1^ o…

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9386Logic and foundationsOpen

Erdős #1171 · set theory / ramsey theory

Is it true that, for all finite k< omega , omega 1^2 to ( omega 1 omega, 3, ldots,3) k+1 ^2?

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9385Logic and foundationsOpen

Erdős #1170 · set theory / ramsey theory

Is it consistent that omega 2 to ( alpha) 2^2 for every alpha < omega 2 ?

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9384Logic and foundationsOpen

Erdős #1168 · set theory / ramsey theory

Prove that aleph omega+1 not to ( aleph omega+1 , 3, ldots,3) aleph 0 ^2 without assuming the generalised continuum hypothesis.

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9383Logic and foundationsOpen

Erdős #1167 · set theory / ramsey theory

Let r geq 2 be finite and lambda be an infinite cardinal. Let kappa alpha be cardinals for all alpha< gamma . Is it true that 2^ lambda to ( kappa alpha+1) alpha< gamma ^ r+1 implies lambda…

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9100Logic and foundationsOpen

Erdős #623 · set theory

Let X be a set of cardinality aleph omega and f be a function from the finite subsets of X to X such that f(A) not in A for all A . Must there exist an infinite Y subseteq X that is independent - that is…

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9088Logic and foundationsOpen

Erdős #598 · set theory / ramsey theory

Let m be an infinite cardinal and kappa be the successor cardinal of 2^ aleph 0 . Can one colour the countable subsets of m using kappa many colours so that every X subseteq m with lvert X rvert= kappa …

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9084Logic and foundationsOpen

Erdős #593 · set theory / graph theory

Characterize those finite 3-uniform hypergraphs which appear in every 3-uniform hypergraph of chromatic number aleph 0 .

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9083Logic and foundationsOpen

Erdős #592 · set theory / ramsey theory

Determine which countable ordinals beta have the property that, if alpha= omega^ ^ beta , then in any red/blue colouring of the edges of K alpha there is either a red K alpha or a blue K 3 .

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-8662Logic and foundationsStatus unassessed