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Regular Languages and Model Theory 30: Axiomatizing WS1S
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In this video, I walk through my axiomatization of the weak monadic second order theory of 1 successor and prove that it is a complete axiomatization: every true fact in the language of WS1S is a logical consequence of my axioms.
00:00 Introduction
01:17 Seifkes' Axiomatization
06:30 Linear Ordering Axioms
12:40 Set Properties
17:08 Closure Under Run Maps
23:08 Every Set Has a Minimal Element
29:30 Uniqueness of Runs
32:25 Successor Automaton Works Correctly
37:53 Closure Under Reverse Run Maps
39:00 Proving Axiomatization is Complete
53:03 Next Video
00:00 Introduction
01:17 Seifkes' Axiomatization
06:30 Linear Ordering Axioms
12:40 Set Properties
17:08 Closure Under Run Maps
23:08 Every Set Has a Minimal Element
29:30 Uniqueness of Runs
32:25 Successor Automaton Works Correctly
37:53 Closure Under Reverse Run Maps
39:00 Proving Axiomatization is Complete
53:03 Next Video
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