The cellar

This page will contain links to summary accounts of supporting foundational or background material used on the rest of the site.

You may like to begin in the playroom for an entertaining introduction to infinity.

Meanwhile, we expect that this page and these resources will be expanded as Cantor's attic develops.

Definition of infinity

• Short informal presentation of the concept of infinity.
• The first steps towards infinity.

Elementary set-theoretic topics

• transitive
• Basic Order Theory
• ordinal
• successor ordinal
• limit ordinal
• cardinality
• axiom of choice
• stationary, club
• Hereditary cardinality
• ultrafilter, measure
• ultrapower
• Partition property
• model

Axiomatic set theories

• Morse-Kelley set theory
• Zermelo-Fraenkel set theory
• Positive set theory
• Kripke-Platek set theory

Forcing

• forcing
• Boolean-valued models
• Boolean ultrapowers

Canonical inner models

• The core model
• The canonical model $L[\mu]$ of one measurable cardinal
• HOD, generic HOD (gHOD)
• mantle (=generic Mantle)
• The constructible universe