[Verse 1] In the realm of logic where structures align Model theory shows us truth by design Compactness theorem keeps our proofs contained While Löwenheim-Skolem shows size can be changed Types and stability guide our way Through infinite models day by day [Chorus] Logic and foundations, building math's core Model, compute, construct and more From Turing's machines to cardinal heights Set theory forcing new insights Cut elimination makes proofs clean The deepest math you've ever seen [Verse 2] Turing machines compute with tape so long Degrees of hardness help us sort what's strong Arithmetical hierarchy climbs up high Each level harder than the one we try Decidable problems have algorithms true Undecidable ones will puzzle you [Chorus] Logic and foundations, building math's core Model, compute, construct and more From Turing's machines to cardinal heights Set theory forcing new insights Cut elimination makes proofs clean The deepest math you've ever seen [Bridge] Large cardinals tower beyond our count Forcing techniques surmount Independence results shake what we know ZFC can't prove which way they go Cohen showed us continuum's free Neither true nor false it has to be [Verse 3] Proof theory cuts away the excess fat Ordinal analysis shows where strength is at Reverse mathematics finds the axioms needed For theorems to be completed Constructive math builds step by step No excluded middle, promises kept [Chorus] Logic and foundations, building math's core Model, compute, construct and more From Turing's machines to cardinal heights Set theory forcing new insights Cut elimination makes proofs clean The deepest math you've ever seen [Verse 4] Intuitionism questions classical thought Type theory builds what can be caught Topos theory foundations unite Category theory's guiding light Homotopy types with paths between Univalence axiom, frontier unseen [Outro] Higher inductive types reach for the sky Logic and foundations will never die From models to machines to types that flow The deepest truths are here to know
← Path 10: Applied Mathematics & Computation | Cross-Cutting Themes →