Translation:I will show this american woman my city on the map.
No, "свой" is a possessive pronoun means "one's own":
- Я ем своё я́блоко (my own apple)
- Я ем его́ я́блоко (his apple)
- Он ест своё я́блоко (his own apple)
- Он ест его́ я́блоко (someone else's apple)
- Он ест моё я́блоко (my apple)
Of course, "свой" is fully declinable:
- Он говори́т о свое́й ко́шке (fem., prep.)
- У них нет свои́х ко́шек (gen.pl.)
Yeah pretty much in agreement. The only thing that was confusing was mentioning two people, and how свой is closer in proximity to американке than it is to я.
Something like "Я показал другу моей жены свой стол" would make me think for a very long time about whose table it was. Is it mine? Is my wife's? Is it her friend's?
This fails to answer the question. It could be "I will show this American her own city on the map". How do you know it is not this? That is why ryandward asked about it only referring to the subject of the sentence.
If you use "её", how do you know it refers to the American and not someone else?
It absolutely could not mean that. «Свой» only refers back to the subject.
As for the second part of your post, it is the same in English and many other languages. Unless there is more information regarding clarification, saying “her” or «её» could mean her own or another woman’s city.
- infinitive: пока́зывать (imperfective) / показа́ть (perfective)
- 1st p. sing. future: я бу́ду пока́зывать (imperfective) / я покажу́ (perfective)
Very awkward English because of the presence of "on the map". "I will show my city to this American" is quite decent English. The problem is you have to make certain that the phrase "on the map" is in exactly the right place so that it attaches to the correct words in the correct order.
For example, "I will show my city to the woman on the map" sounds like the woman" is "on the map", rather than "to show on the map".
Also, because of "on the map" you have to use "show the woman" rather than "show to the woman".
It's really a question of English idiomatic word-order in an English sentence which requires a fairly specific order in order to be idiomatic. This one is particular troublesome for non-native-Engish speakers.
Dative, I believe. "свой город" is in Accusative because that is what's being shown, and it is being shown to "этой американке", which would require Dative. Then "на карте" would require Prepositional, because it refers to where the city is being shown to the American girl.
I think I've finally gotten these cases down... =D If anyone finds any flaws in my evaluation, please point them out! Thanks!