The singular cardinals hypothesis, henceforth SCH, states that if $\kappa$ is a singular strong limit cardinal (i.e., cf($\kappa$) < $\kappa$ and for all $\lambda < \kappa, 2^\lambda < ...
transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
The cardinal numbers (or just cardinals) constitute a generalisation of natural numbers to numbers of possibly infinite magnitudes. Specifically, cardinal numbers generalise the concept of ‘the number of …’. In parti…
