Absolute definition of 'True' and 'False' in Mathematical Logic I searched for the definition of Truth.
According to this Wikipedia: https://en.m.wikipedia.org/wiki/Truth ,

Truth is the property of being in accord with fact or reality.


when I searched for the definition of fact and reality,
according to this Wikipedia: https://en.m.wikipedia.org/wiki/Fact ,

A fact is something that is true.

according to this Wikipedia: https://en.m.wikipedia.org/wiki/Reality

Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that which is only imaginary.


So, I feel that this is not an absolute definition of 'True' and 'False'.
Is there a logical derivation of the definition of 'logical true' and 'logical false'?
 A: When in real life we talk about something being 'True', we mean that it is the case in the world that we live in.  Thus, for example, we say that "Bananas are yellow" is True, but "I can swim across the Atlantic Ocean" is False.
So this is all compatible with the definitions you found on Wikipedia; this is all about facts and what is real: it's about our world.
In Mathematical Logic, however, we can contemplate any world we want. So there we can consider worlds where bananas are not yellow, but purple, or worlds where I can swim across the Atlantic. By 'any world we want' we mean any logically possible world ... basically an worlds that we can coherently imagine ... can you imagine a world where bananas are purple? Sure! But we may want to rule out worlds where a banana is both purple and not purple at the same time ... At least classical logic will say such a world is not logically possible.
So, many of these worlds are imaginary or idealized worlds. As such, whether some given statement is 'True' or 'False' in mathematical Logic depends on which of these worlds we evaluate the sentence in. That is, truth is relative to a world. The same statement can be True in one world, but False in another.
Indeed, logic (and much of mathematics, actually) really doesn't care so much about truth, as it cares about implication. So we say things like: Sentence $\phi$ implies sentence $\psi$, by which we mean: in all logically possible worlds , if $\phi$ is true, then $\psi$ is true as well.  So, whether statements are actually True (i.e. in our world), logic doesn't care about, but since it does care about implication, it needs to consider all kinds of worlds, and the truth-value of any statement can change between those worlds.
Finally, look at the link Mauro put in the first Comment to see how truth-in-a-world is dealt with in Mathematical Logic through the notion of an Interpretation. Lots of details there, though most of it deals with the syntactical and grammatical nature of the language of formal/mathematical logic. In the end, we simply take our basic/atomic statements, and we simply declare those to be true or false in our world (pretty much as a way to create that world in the first place) and go from there. There is really nothing deeper than that... which might make you a little disappointed, but hey, we need to start somewhere: if you keep asking why, you get turtles all the way down, and it'll never stop.
