A general pattern for contradictions by self-reference

TODO

So Tarski, Turing, Godel and Russel all use the same pattern.

Regarding Halting:

A function H(h,x) determines if program h halts given input x.

Now we can construct I(h,x) which goes into a loop if H(h,x) says 'h' doesn't and vice-versa.

So what about H(I,I)?

If H says it halts we know that 'I' will loop and vice versa.

As usual I need tidy up the logic.

Regarding Tarski:

A function T(t,x) determines if theorem 't' is true given x.

Now we can construct U(t,x) which states the opposite. So that U(t,x) is false if t(x) is true.

So what about T(U,U).

And again with Provability for Godel and Selfincludes for Russel.

Tidy the logic up here.

Now is this the basis for Contradiction by Self-Reference.

If a statement can be transformed into this format it's game over?

Can all self-contradictory statements get into this format.

Are all other formats safe from self-contradiction?