And my definition of synchronism is that A knows what time B is showing, just from observing his own clock and nothing else.Why bring up synchronism? The word seems irrelevant to this topic unless you mean it to be a synonym for synchronized, which it isn't. Your definition doesn't match how that word is normally used, which at best might be a synonym for 'simultaneious', or maybe the coordination of something like video and its soundtrack, two things in the same place.
Something is called a paradox if it seems like there's a contradiction, but a closer look can determine that there are errors in the line of thought leading to that contradiction.That would be a seeming paradox, not an actual paradox. The liars paradox (probably the simplest one) has no logical errors leading to the contradiction that makes it an actual paradox.
On the other hand, if the contradiction is inherently within the described situation, and no error can be found in the reasoning, then the conclusion is to reject the proposition. It's called proof by contradiction.Yes, that would simply be a false proposition, not a paradoxical one.
You wonderfully illustrate such a contradiction with your following statement:
Twin paradox is called paradox by those who accept STR. They think that it doesn't cause a real contradiction.This is a self-contradictory statement. If they think (correctly or not) theory X has no contradictions, then rationally they would not call it paradoxical. But your statement says those that accept theory X find a prediction made by X to be paradoxical. So you assertion is proven false by contradiction.
Are you of the opinion that STR is not self consistent? Because you've not actually identified any problem.
On the other hand, critics of STR think that twin paradox actually demonstrate a contradiction, instead of just a paradox. It causes them to reject STR.Sure, but those critics don't know their physics, or worse, they do know it, but the deliberately misrepresent it. There are whole websites dedicated to that sort of thing, and publishing such deliberately wrong tripe helps gain acceptance among the troll peers that socialize around such sites.
My favorite are the articles claiming STR does not predict the Sagnac effect, and it's pretty trivial to spot the errors in these papers. Why does light travel west faster than it does east? Can you explain that in STR terms without violating its premise about the constancy of light speed?