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Zuhair Al-Johar
Zuhair Al-Johar
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Can we have a consistent and effective (fulfilling Godel's criteria) first order theory $T$, that is both arithmetically unsound and $\omega$-inconsistent, and yet doesn't prove its own inconsistency ( i.e. $T \not \vdash \neg \operatorname {Con}(T)$)?

Can we have a consistent and effective (fulfilling Godel's criteria) first order theory $T$, that is both unsound and $\omega$-inconsistent, and yet doesn't prove its own inconsistency ( i.e. $T \not \vdash \neg \operatorname {Con}(T)$)?

Can we have a consistent and effective (fulfilling Godel's criteria) first order theory $T$, that is both arithmetically unsound and $\omega$-inconsistent, and yet doesn't prove its own inconsistency ( i.e. $T \not \vdash \neg \operatorname {Con}(T)$)?

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Zuhair Al-Johar
Zuhair Al-Johar
  • 11.3k
  • 1
  • 13
  • 47

Is there a consistent, unsound, $\omega$-inconsistent, effective theory $T$ that doesn't prove its own inconsistency?

Source Link
Zuhair Al-Johar
Zuhair Al-Johar
  • 11.3k
  • 1
  • 13
  • 47

Is there a consistent, unsound, $\omega$-inconsistent, effective theory $T$ that doesn't prove its own inconsistency?

Can we have a consistent and effective (fulfilling Godel's criteria) first order theory $T$, that is both unsound and $\omega$-inconsistent, and yet doesn't prove its own inconsistency ( i.e. $T \not \vdash \neg \operatorname {Con}(T)$)?