Add Erdős Problem 1128 (Prikry-Mills counterexample for monochromatic countable boxes)#3782
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Formalises Problem 1128 on monochromatic countable boxes in 2-colourings of ω × ω × ω₁. The main theorem answers False via the Prikry-Mills (1978) construction, recorded as the unpublished lemma prikryMills (with `sorry`). Includes variants.two_dimensional_false formally disproving the naturally-false two-dimensional variant via the ordering colouring, plus four proved helper lemmas establishing countability and boundedness properties of ω₁. Reference: https://www.erdosproblems.com/1128 Assisted by Claude (Anthropic).
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Formalises Erdős Problem 1128: whether every 2-colouring of$\omega \times \omega \times \omega_1$ admits a monochromatic product $A \times B \times C$ with $A, B, C$ countably infinite.
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False): the problem is resolved negatively via the Prikry-Mills (1978, unpublished) construction.prikryMillslemma (sorry): records the unpublished 1978 Prikry-Mills counterexample colouring.variants.two_dimensional_false: a formal disproof of the naturally-false two-dimensional variant using the ordering colouring oncard_le_aleph0_of_lt_omega1,countable_toType_of_lt_omega1,countable_Iio_of_lt_omega1,countable_Iio_omega1,countable_subset_bdd) used for the supporting infrastructure.Assisted by Claude (Anthropic).