1. September 27, 2013.The End of TimePage: 1

2. The end of Time (defining time and space) Hajnal Andréka and István Németi

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4. September 27, 2013.The End of TimePage: 4 We have experimenters communicating with each other. Observing the the laws of this communication, they create the concepts of time and space in order to act in this world more effectively.

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7. September 27, 2013.The End of TimePage: 7 No clocksNo meter rods

8. September 27, 2013.The End of TimePage: 8 Experimenters Signals Connects(e,s,e’) s e’ e Experimenters and signals in a concrete spacetime

9. September 27, 2013.The End of TimePage: 9 Signals Experimenters Connects(e,s,e’) s e’ e e e' s Experimenters know only this Goal to find out

10. September 27, 2013.The End of TimePage: 10 s e’ e e e' s Experimenters know only this Bare, puritan model Rich, structured model Getting familiar s a’ a a z z

11. What is SPACE? September 27, 2013.The End of TimePage: 11

12. Motionless 1 September 27, 2013.The End of TimePage: 12

13. Motionless 2 September 27, 2013.The End of TimePage: 13 e e’

14. September 27, 2013.The End of TimePage: 14 Desargues’s theorem

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16. September 27, 2013.The End of TimePage: 16 By now experimenters have meter rods.

17. What is TIME? September 27, 2013.The End of TimePage: 17

18. September 27, 2013.The End of TimePage: 18 Event = congruence class of sending and receiving signals “at the same time” z s s’ e e’ e sends s ≡ e’ sends z ≡ e receives s’ ≡ …

19. September 27, 2013.The End of TimePage: 19 Order of events Equi-duration of time-lapses Addition Multiplication.

20. September 27, 2013.The End of TimePage: 20 Multiplication

21. September 27, 2013.The End of TimePage: 21 By now experimenters have clocks.

22. September 27, 2013.The End of TimePage: 22 Using these concepts, our experimenters can observe finitely many regularities between the events (they can state them to be physical laws) such that on the base of this they can know that their space-time is a 4-dimensional space over a field F. Formally, this amounts to a finite set Sigma in the language of the bare models such that the models of Sigma are exactly “our bare models” with an arbitrary field F in place of the field of reals. If they add the finite schema of axioms for a real-closed field, they can derive everything that is true in their world.

23. September 27, 2013.The End of TimePage: 23 Direction of time Schwarzschild black hole Operational semantics for SpecRel Interpretation between theories Comparing theories Ontology of concepts. Infinity of things to say yet:

24. THE END September 27, 2013.The End of TimePage: 24 OF TIME as a basic notion

25. Thank you for your attention! September 27, 2013.The End of TimePage: 25